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• W2108857780 abstract "In this paper we study the degree sequence of the permutation graph $G_{pi_n}$ associated with a sequence $pi_nin S_n$ of random permutations. Joint limiting distributions of the degrees are established using results from graph and permutation limit theories. In particular, for the uniform random permutation, the joint distribution of the degrees of the vertices labelled $lceil nr_1 rceil, lceil nr_2 rceil, ldots, lceil nr_s rceil$ converges (after scaling by $n$) to independent random variables $D_1, D_2, ldots, D_s$, where $D_isim text{Unif}(r_i, 1-r_i)$, for $r_iin [0,1]$ and $iin {1, 2, ldots, s}$. Moreover, the degree of the mid-vertex (the vertex labelled $n/2$) has a central limit theorem, and the minimum degree converges to a Rayleigh distribution after appropriate scalings. Finally, the limiting degree distribution of the permutation graph associated with a Mallows random permutation is determined, and interesting phase transitions are observed. Our results extend to other exponential measures on permutations." @default.
• W2108857780 created "2016-06-24" @default.
• W2108857780 creator A5052870102 @default.
• W2108857780 creator A5082129067 @default.
• W2108857780 date "2015-03-12" @default.
• W2108857780 modified "2023-09-27" @default.
• W2108857780 title "DEGREE SEQUENCE OF RANDOM PERMUTATION GRAPHS" @default.
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• W2108857780 hasPublicationYear "2015" @default.
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